Mathematical Aspects of Logic Programming Semantics -

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Résumé :
Presenting the methods required to study the semantics of logic programs, this book significantly extends these tools from the order theory traditionally used in the subject to include nontraditional methods depending on topology, generalized distance functions, and their associated fixed-point theory. The authors provide a self-contained, detailed overview of the development of both conventional and nonconventional methods and techniques, fulfilling a significant gap in the literature on theoretical computer science. They examine the interaction between logic programming and connectionist systems from the point of view of semantics.

Biographie:
Pascal Hitzler is an assistant professor in the Kno.e.sis Center for Knowledge-Enabled Computing, which is an Ohio Center of Excellence at Wright State University. Dr. Hitzler is editor-in-chief of the journal Semantic Web - Interoperability, Usability, Applicability and co-author of the textbook Foundations of Semantic Web Technologies (CRC Press, August 2009). His research interests encompass the Semantic Web, neural-symbolic integration, knowledge representation and reasoning, denotational semantics, and set-theoretic topology. Anthony Seda is a senior lecturer in the Department of Mathematics and co-founder of the Boole Centre for Research in Informatics at University College Cork. Dr. Seda is an editorial board member of Information and the International Journal of Advanced Intelligence. His research interests include measure theory, functional analysis, topology, fixed-point theory, denotational semantics, and the semantics of logic programs.

Sommaire:
Order and Logic Ordered Sets and Fixed-Point Theorems First-Order Predicate Logic Ordered Spaces of Valuations The Semantics of Logic Programs Logic Programs and Their Models Supported Models Stable Models Fitting Models Perfect Models Well-Founded Models Topology and Logic Programming Convergence Spaces and Convergence Classes The Scott Topology on Spaces of Valuations The Cantor Topology on Spaces of Valuations Operators on Spaces of Valuations Revisited Fixed-Point Theory for Generalized Metric Spaces Distance Functions in General Metrics and Their Generalizations Generalized Ultrametrics Dislocated Metrics Dislocated Generalized Ultrametrics Quasimetrics A Hierarchy of Fixed-Point Theorems Relationships between the Various Spaces Fixed-Point Theory for Multivalued Mappings Partial Orders and Multivalued Mappings Metrics and Multivalued Mappings Generalized Ultrametrics and Multivalued Mappings Quasimetrics and Multivalued Mappings An Alternative to Multivalued Mappings Supported Model Semantics Two-Valued Supported Models Three-Valued Supported Models A Hierarchy of Logic Programs Consequence Operators and Fitting-Style Operators Measurability Considerations Stable and Perfect Model Semantics The Fixpoint Completion Stable Model Semantics Perfect Model Semantics Logic Programming and Artificial Neural Networks Introduction Basics of Artificial Neural Networks The Core Method as a General Approach to Integration Propositional Programs First-Order Programs Some Extensions - The Propositional Case Some Extensions - The First-Order Case Final Thoughts Foundations of Programming Semantics Quantitative Domain Theory Fixed-Point Theorems for Generalized Metric Spaces The Foundations of Knowledge Representation and Reasoning Clarifying Logic Programming Semantics Symbolic and Subsymbolic Representations Neural-Symbolic Integration Topology, Programming, and Artificial Intelligence Appendix: Transfinite Induction and General Topology The Principle of Transfinite Induction Basic Concepts from General Topology Convergence Separation Properties and Compactness Subspaces and Products The Scott Topology Bibliography Index